The compactness parameter of a body of mass and radius is

PHYSICS · Subjective · Fermi University Physics · Relativity & Gravitation · Relativistic stars and compact objects · Relativistic stars and compact objects

Relativity and Gravitation, Ch Escape velocity, the Schwarzschild radius and the idea of a black hole

Problem

The compactness parameter of a body of mass

M

and radius

R

GM/Rc^2

. Four bodies have the following masses and radii. Jupiter:

M = 1.898 \times 10^{27}\ \mathrm{kg}

R = 6.99 \times 10^{7}\ \mathrm{m}

; the Sun:

M = 1.989 \times 10^{30}\ \mathrm{kg}

R = 6.96 \times 10^{8}\ \mathrm{m}

; the white dwarf Sirius B:

M = 2.03 \times 10^{30}\ \mathrm{kg}

R = 5.85 \times 10^{6}\ \mathrm{m}

; a neutron star:

M = 2.785 \times 10^{30}\ \mathrm{kg}

R = 1.20 \times 10^{4}\ \mathrm{m}

. Compute the compactness parameter of each and list the four values in increasing order of compactness. Use

G = 6.674 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}

and

c = 2.998 \times 10^{8}\ \mathrm{m\,s^{-1}}

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